Localization of invariant compact sets of discrete systems (Q606588)

A functional method for localizing invariant compact sets for continuous dynamical systems is extended to one-dimensional discrete dynamical systems. The idea is to construct a localizing set, that is, the set that contains all invariant compact sets of a given system. The properties of localizing sets for discrete dynamical systems are formulated for positively invariant sets. These are similar to corresponding properties for continuous dynamical systems; analogous assertions can be also formulated for negatively invariant and invariant compact sets.